If a circular disk is rotated at high speed (for example, 50 thousand RPM) the disk will expand radially. If the disk has a hole in the center to accommodate a drive shaft, high speed rotation will cause the center hole to expand. The expansion of the center hole of the disk results in stresses distributed around the hole in the center of the disk.
In many centrifuges, the rotor is bolted to a hub which is in turn driven by a spindle or shaft. If a rotor is bolted to a hub, the bolt holes create both radial and tangential stress patterns. The bolts not only hold the rotor down and gives it tangential force necessary to cause rotation, but they also constrain the center portion of the rotor from moving outward as the centrifugal forces expand the radius of the rotor. This introduces additional stresses into the rotor, particularly around the bolt holes.
In the prior art this problem was addressed by providing a substantially solid hub which was reinforced as required to tolerate the centrifugal stresses generated with neglible strain at the hub, thus allowing for a rigid assembly and concentricity as required for dynamic stability. In many instances the problem was addressed by a combination of making the rotor strong enough to withstand the stress by reducing strain and by removing material from the rotor to reduce the centrifugal forces. For example in the device shown in U.S. Pat. No. 4.350.283 (Leonian) the material has been removed to the extent that the rotor essentially consists of a bar which has a disk under the bar to impart stability to the structure.
Another factor that introduces stress points into a rotor is that rotors generally include tubes that interconnect the separation chamber. Space for these tubes could be provided by having a hole through the disk or by having a slot cut partway through the rotor. Such discontinuities in a rotor introduce further stresses because the portion of the disk with the hole or slot tends to expand at one rate whereas the other portion of the rotor expands at a different rate and hence, in addition to the tangential and radial forces, bending forces are introduced into the rotor resulting in complex stress distribution patterns.
Stress analysis techniques are well known: however, two dimensional stress analysis as applied to a substantially symmetrical design is a much faster operation than is three dimensional stress analysis. Rotors which have asymmetrical features such as holes and openings to facilitate tubing generally require a time consuming three dimensional analysis process followed by complex solutions.